Stochastic comparison results between two finite mixture models with generalized Weibull distributed components
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Bibliographic record
Abstract
In this paper, we establish sufficient conditions for stochastic comparisons of two finite mixture models (FMMs) with respect to the usual stochastic order, hazard rate order, and likelihood ratio order when the mixing components have generalized Weibull family of distributions. The established (sufficient) conditions are mainly based on the majorization order, weak supermajorization order, and weak submajorization order. The stochastic comparisons are studied when there is heterogeneity in one (model) parameter, and then in two parameters (model parameter and mixing proportion). Further, the concept of unordered majorization order is employed to establish the usual stochastic order between two FMMs. To illustrate the theoretical results established here, several numerical examples and counterexamples are presented. Finally, we have generalized some of the results to the case of τ-mixture models.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it